Low side or high side control

 Low side or high side topologies are common for loads controlled from both AC or DC power supplies, but they make more sense if there is a unidirectional flow of electric charge (DC)

Implementations are related to different switching technologies available: bipolar (PNP, NPN), MOS (P - channel / N - channel), relay...

Usually low side implementations are simpler.

Combining low side and high side switches:
Half bridge or Half-H

The half bridge is a combination of high side and low side switches. Used in some switched-mode power supplies that use synchronous rectifiers and in switching amplifiers. A double switch for the same load can be used as a fail proof technique.

Full bridge or H bridge or Full-H

 An H bridge is an electronic circuit that enables a voltage to be applied across a load in either direction composed by pairs of low side high side switches. An H bridge is built with four switches (solid-state or mechanical). When the opposing switches S1 and S4 are closed and S2 and S3 are open a positive voltage will be applied across the load. By opening S1 and S4 switches and closing S2 and S3 switches, this voltage is reversed, allowing reverse operation of the load.
Common uses of the H bridge are DC motor control and inverters.
Multi phase control
Topologies that combine more than one power supply and more than one load.